Abstract
Energy-level densities are key for obtaining various chemical properties. In chemical kinetics, energy-level densities are used to predict thermochemistry and microscopic reaction rates. Here, an analytic energy-level density formulation is derived using inverse Laplace transformation of harmonic oscillator partition functions. Anharmonic contributions to the energy-level density are considered approximately using a literature model for the transition from harmonic to free motions. The present analytic energy-level density formulation for rigid rotor-harmonic oscillator systems is validated against the well-studied CO+O˙H system. The approximate hindered rotor energy-level density corrections are validated against the well-studied H2O2 system. The presented analytic energy-level density formulation gives a basis for developing novel numerical simulation schemes for chemical processes.
Highlights
The concept of energy-level densities is used throughout physics to describe e.g. semiconductors in condensed-matter physics,[1] proteins in bio-physics,[2] and chemical reactions in gas-phase kinetics.[3]
For chemical reactions in particular, the Rice-Ramsperger-Kassel-Marcus (RRKM) theory has emerged as state-of-the-art formulation for microscopic reaction probabilities
The present work provided an analytic formula for vibrational energy-level densities, satisfying their continuous nature
Summary
The concept of energy-level densities is used throughout physics to describe e.g. semiconductors in condensed-matter physics,[1] proteins in bio-physics,[2] and chemical reactions in gas-phase kinetics.[3]. It would be possible to describe zero-dimensional chemical processes using energy-level densities for RRKM and thermochemistry exclusively This would increase the computational efforts required for simulations, using energy-level density-based simulation schemes would significantly improve the prediction of chemical processes. While for numerical simulations of the high-pressure limit the use of energy-level densities would not change the thermochemistry or kinetics, recent theoretical kinetic studies point towards the need for energy-resolved numerical simulations if not in the high-pressure limit.[23,24,25,26,27,28] The formation and consumption of non-thermal intermediates appears to be of high importance under high-temperature and low-pressure conditions These effects, are mostly neglected presently and are hard to implement in state-of-the-art numerical simulation schemes. A concluding discussion on the benefits from the presented data format provides insights to potential future numerical simulation frameworks
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